{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Decision Tree Classifiers\n",
    "<p>This Notebook gives an overview of DecisionTrees with scikit learn. In it are examples of:\n",
    "\n",
    "<ul>\n",
    "<li>Build a basic decision tree</li>\n",
    "<li>Plotting the decision surface of a decision tree</li>\n",
    "<li>Visualing the decision tree</li>\n",
    "<li>Overfitting (as viewed by decision surfaces) of decision trees with no limits on depth and leaf size</li>\n",
    "<li>Searching for optimal parameters of a decision tree</li>\n",
    "<li>Using decision tree output to assess feature importance</li>\n",
    "</ul>\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Build a Tree on Simulated Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#These all need to be installed to both run and visualize a tree\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.tree import export_graphviz\n",
    "from IPython.display import Image\n",
    "import StringIO, pydot\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here I generate some random data $X=<X1,X2>$ with $Y \\in [0,1]$\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x108c7c590>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A60vVxjc4yINl3zPPD9g8FvmyvnhcLgzTvn8g/EVI2AMgJ1ESb3A3s5Iqdjd0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108bcca50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "Random data example \n",
    "'''\n",
    "n=200\n",
    "\n",
    "\n",
    "#First Generate the data\n",
    "\n",
    "m=[[0.25,0.75],[0.75,0.75],[0.75,0.25],[0.25,0.25]]\n",
    "s=.1\n",
    "X1=pd.DataFrame(np.random.multivariate_normal([m[0][0],m[0][1]],[[s,0],[0,s]],n), columns=['x1','x2'])\n",
    "X1['y']=np.zeros(n)\n",
    "X2=pd.DataFrame(np.random.multivariate_normal([m[1][0],m[1][1]],[[s,0],[0,s]],n), columns=['x1','x2'])\n",
    "X2['y']=np.zeros(n)\n",
    "X3=pd.DataFrame(np.random.multivariate_normal([m[2][0],m[2][1]],[[s,0],[0,s]],n), columns=['x1','x2'])\n",
    "X3['y']=np.ones(n)\n",
    "X4=pd.DataFrame(np.random.multivariate_normal([m[3][0],m[3][1]],[[s,0],[0,s]],n), columns=['x1','x2'])\n",
    "X4['y']=np.zeros(n)\n",
    "\n",
    "dat=X1.append(X2,ignore_index=True)\n",
    "dat=dat.append(X3,ignore_index=True)\n",
    "dat=dat.append(X4,ignore_index=True)\n",
    "\n",
    "plot(dat['x1'][(dat['y']==1)],dat['x2'][(dat['y']==1)],'r.')\n",
    "plot(dat['x1'][(dat['y']==0)],dat['x2'][(dat['y']==0)],'b.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>\n",
    "Now lets build a tree on our sample data.<br><br>\n",
    "\n",
    "Documentation can be found here:\n",
    "http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier\n",
    "<br>\n",
    "Also, here is another useful example:\n",
    "http://nbviewer.ipython.org/github/sujitpal/statlearning-notebooks/blob/master/src/chapter8.ipynb\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#We want Entropy as our splitting criteria\n",
    "clf = DecisionTreeClassifier(criterion='entropy',min_samples_leaf=1,max_depth=3)\n",
    "clf = clf.fit(dat.drop('y',1), dat.y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Building a tree is pretty easy. Visualizing the tree takes a little extra work and a few extra packages.<br><br>\n",
    "To plot it is necessary to install Pydot as well as graphviz: http://www.graphviz.org/\n",
    "If you have homebrew installed, run: brew install graphviz in the command line.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PnPd/TFpurRvPfqOt4sWLOyajlGMCC+s90YedO3e6/fLvmOC+zsknn+wvDjg2yiPHZHFy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Kt/jjKDzsGeeuop823jMqhHf+ndu7fAiZiG2JN///vf7lbCUcNfSvv27f20OP1zmdXzumhIcGnd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M12VjgPdEgcviDgoXIEaGIR+yRNm3YBBkmCpeOWXKFJXviGOW/m7hSo4iJJ0GTroFFivAP7w8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\nrkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image at 0x1090b8d10>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot_data = StringIO.StringIO()\n",
    "export_graphviz(clf, out_file=dot_data)\n",
    "graph = pydot.graph_from_dot_data(dot_data.getvalue())\n",
    "Image(graph.create_png())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The decision surface can be derived by using the predict function and not having to parse the DT rules.<br><br>\n",
    "This code was adapted from http://scikit-learn.org/0.11/auto_examples/tree/plot_iris.html\n",
    "\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x105cc60d0>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YsSOfJgclVsLW7MvoRTD7nfnOqSD2MmnJ56m++pbmGW1DshoYBnunTaS3RpX0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\nQIRwFwgEggrk/wf6xoWyYwympwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109b5f390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=dat.drop('y',1)\n",
    "y=dat.y\n",
    "\n",
    "plot_step = 0.02\n",
    "\n",
    "x_min, x_max = X['x1'].min(), X['x1'].max()\n",
    "y_min, y_max = X['x2'].min(), X['x2'].max()\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),np.arange(y_min, y_max, plot_step))\n",
    "\n",
    "Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "\n",
    "\n",
    "plt.subplot(111)\n",
    "\n",
    "cs = plt.contourf(xx, yy, Z, cmap=plt.cm.cool)\n",
    "plt.plot(dat['x1'][(dat['y']==1)],dat['x2'][(dat['y']==1)],'r.')\n",
    "plt.plot(dat['x1'][(dat['y']==0)],dat['x2'][(dat['y']==0)],'b.')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The above is a pretty simple tree, which we can see in the above plot.<br><br>\n",
    "\n",
    "As we allow for more complex trees, visualing the tree becomes very cumbersome, but we can still look at the decision surface. \n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4+/sjKiqqU/vNmzcxb948jBgxApMmTUJhYaHDZa1YsQK//e1v+7R/5eXl2Llz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108da9e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def treeComplex(X,y,leaf,dep,i):\n",
    "    clf = DecisionTreeClassifier(criterion='entropy',min_samples_leaf=leaf,max_depth=dep)\n",
    "    clf = clf.fit(X,y)\n",
    "    plot_step = 0.02\n",
    "    x_min, x_max = X['x1'].min(), X['x1'].max()\n",
    "    y_min, y_max = X['x2'].min(), X['x2'].max()\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),np.arange(y_min, y_max, plot_step))\n",
    "    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "\n",
    "    ax = fig.add_subplot(3,3,i)\n",
    "    cs = plt.contourf(xx, yy, Z, cmap=plt.cm.cool)\n",
    "    ax.axes.get_xaxis().set_visible(False)\n",
    "    ax.axes.get_yaxis().set_visible(False)\n",
    "    plt.title('Dep={},Leaf={}'.format(dep,leaf))\n",
    "              \n",
    "leafs=[100,10,1]\n",
    "deps=[3,10,50]\n",
    "\n",
    "i=1\n",
    "fig=plt.figure()\n",
    "\n",
    "for l in leafs:\n",
    "    for d in deps:\n",
    "        treeComplex(dat.drop('y',1),dat.y,l,d,i)\n",
    "        i+=1\n",
    "        \n",
    "fig.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As we let the trees grow without any restrictions, we notice that the decision surface gets very fragmented. This defies our intuition that nearest neighbors of a point should have the same class assignment. Since we know that this data was generated from a few simple normal mixtures, we should understand that these more complex surfaces are terribly over fit.\n",
    "<br><br>\n",
    "Beyond toy examples, let's see this on real data.\n",
    "</p>\n",
    "\n",
    "###Decision Tree on Real Data\n",
    "<p>We don't just want to build a tree, we want to optimize the configuration of the tree. We'll use AUC as a metric on our test set and vary the max_depth and min_leaf_size. <br><br>\n",
    "\n",
    "The underlying data has a very rare outcome (less than 5%) so we'll down sample the data first to reach a 50/50 split.\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix,roc_auc_score\n",
    "import course_utils as bd\n",
    "reload(bd)\n",
    "\n",
    "#Load data and downsample for a 50/50 split, then split into a train/test\n",
    "f='/Users/briand/Desktop/ds course/datasets/ads_dataset_cut.txt'\n",
    "\n",
    "train_split = 0.5\n",
    "tdat = pd.read_csv(f,header=0,sep='\\t')\n",
    "\n",
    "moddat = bd.downSample(tdat,'y_buy',9)\n",
    "#We know the dataset is sorted so we can just split by index\n",
    "train = moddat[:int(math.floor(moddat.shape[0]*train_split))]\n",
    "test = moddat[int(math.floor(moddat.shape[0]*train_split)):]\n",
    "\n",
    "def testTrees(X_train,y_train,X_test,y_test,dep,leaf,auc):\n",
    "    clf = DecisionTreeClassifier(criterion='entropy',min_samples_leaf=leaf,max_depth=dep)\n",
    "    clf = clf.fit(X_train,y_train)\n",
    "    if (auc==0):\n",
    "        cm = confusion_matrix(clf.predict(X_test),y_test)\n",
    "        return (cm[0][0]+cm[1][1])/float(sum(cm))\n",
    "    else:\n",
    "        return roc_auc_score(y_test,clf.predict_proba(X_test)[:,1])\n",
    "    \n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10b01b610>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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a+XuR6X4N/EI4LTEQDZYZieU7l4suXfQ/x9Wo08JhsUpoNDlCdOggxL//lqyQ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\nEGKx/wPn65CAXE7PFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10994c190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lab='y_buy'\n",
    "\n",
    "depths=[4,5,10,20]\n",
    "leaves=np.arange(1,101)\n",
    "\n",
    "#Run all of the options\n",
    "run=1\n",
    "if (run==1):\n",
    "    #Initialize dictionary of results\n",
    "    res=dict()\n",
    "    for d in depths:\n",
    "        res[d]=list()\n",
    "\n",
    "    #Now train and get results for each option\n",
    "    for d in depths:\n",
    "        for l in leaves:\n",
    "            res[d].append(testTrees(train.drop(lab,1),train[lab],test.drop(lab,1),test[lab],d,l,1))\n",
    "\n",
    "\n",
    "#Now plot            \n",
    "fig = plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "plt.plot(leaves,res[depths[0]],'b-',label='Depth={}'.format(depths[0]))\n",
    "plt.plot(leaves,res[depths[1]],'r-',label='Depth={}'.format(depths[1]))\n",
    "plt.plot(leaves,res[depths[2]],'y-',label='Depth={}'.format(depths[2]))\n",
    "plt.plot(leaves,res[depths[3]],'g-',label='Depth={}'.format(depths[3]))\n",
    "plt.legend(loc=4)\n",
    "ax.set_xlabel('Min Leaf Size')\n",
    "ax.set_ylabel('Test Set AUC')\n",
    "plt.title('Holdout AUC by Hyperparameters')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The above plot shows how holdout AUC varies by parameters. As we generally expect with most hyper-parameter searches, there is a \"sweet spot\" between letting the model be flexible and over fitting. Here we see that as long as we restrict the min_leaf_size, the max_depth doesn't affect the optimal choice too much.<br><br>\n",
    "\n",
    "We might want to peak at the tree to determine which features it thinks are important. The DT class objects actually have an attribute that gives each feature a score for how important it is in building the tree. \n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1067e1f50>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ihBDS4FVbQ3B3d69xX+SoqChuhaqIaghlx4F+hRFp0Wfz5UZNRi8h+qMjDRV9\nNl9uojUZlXf58mVcvXoVhYWFwm2TJk2qfekIIYQ0WGqtdvrnn3/iypUrGDFiBH777Tf07duXEgIh\nhDQyKmcqHzhwAJGRkejQoQOCg4MRHx9Py1cQQkgjpDIhNG/eHJqamtDS0kJ2djbatm2L9PR0KcpG\nCCFEQiqbjFxdXZGVlYXp06fDxcUFOjo6cHNzk6JshBBCJFSrUUYpKSnIzc2Fg4MDzzJVQqOMyo4D\njeQg0qLP5stN9A1yACA+Ph5hYWGIi4vDjRs38PPPP6sdICIiAra2trC2tsaaNWsq3b9r1y44OjrC\nwcEBffr0QUJCgtrnJoQQIh6VNQR/f39cvnwZXbt2hYbG//JHcHCwypPL5XLY2NggMjISJiYmcHV1\nRWhoKOzs7IRjzpw5gy5duqBly5aIiIhAUFCQsF2nUEiqITw/DvQrjEiLPpsvN9HnIZw9exZXrlyp\ncdZydWJjY2FlZQULCwsAgK+vL8LCwpQSQu/evYX/9+rVC7dv3651HEIIIXWnssnI1dUViYmJL3Ty\njIwMmJmZCddNTU2RkZFR7fE//fQT3nzzzReKRQghpG5U1hD8/f3Ru3dvtG/fHk2bNgXwvBqiTlt/\nbWoVUVFR2Lp1K06dOlXl/UFBQcL/3d3d4e7urva5CSHkVRAdHY3o6OgXfrzKhDB16lTs3LkT3bp1\nU+pDUIeJiYnSnIX09HSYmppWOi4hIQHTp09HREQEDAwMqjxX+YRACCGksoo/lpctW1arx6tMCG3b\ntsWoUaNqXTAAcHFxwY0bN5CamgpjY2Ps3bsXoaGhSsekpaXBy8sLO3fuhJWV1QvFIYQQUncqE4KT\nkxPefvtteHh4oEmTJgCeNwV5eXmpPrmWFjZt2oShQ4dCLpdj6tSpsLOzw5YtWwA83695+fLlyMrK\nwsyZMwEA2traiI2NrctzIoQQ8gLUGnZaFXWGnYqFhp2WHQca2kekRZ/Nl5uow07lcjlat26NtWvX\n1rlghBBCGrYae4k1NTVx6tQpyvyEEPIKUKsPYfTo0Rg7dixatGgBQP0+BEIIIS8PlQmhsLAQrVu3\nxokTJ5Rup4RACCGNC+2p3ABQxx1pqOiz+XITfbXT9PR0jBkzBkZGRjAyMoK3tzetN0QIIY2QyoTg\n7++PUaNG4c6dO7hz5w48PDyqHYpKCCHk5aWyycjR0RHx8fEqb+OJmozKjgNVy4m06LP5chO9yahN\nmzYICQlv9hCVAAAgAElEQVSBXC5HSUkJdu7cCUNDwzoVkhBCSMOjsoaQmpqKwMBAYdMaNzc3bNy4\nEebm5pIUEKAagnAc6FcYkRZ9Nl9utf3upFFGDQD90ZGGij6bLzfRlq6obtlUxR4HS5YsqWXRCCGE\nNGTVJgQdHZ1KG9w8ffoUP/30EzIzMykhEEJII6NWk1FOTg42bNiAn376CePGjcOCBQvQtm1bKcoH\ngJqMhONA1XIiLfpsvtxEXe300aNHWLduHXbt2oVJkybh4sWL1e5oRggh5OVWbUL44IMP8Msvv+Dd\nd99FQkIC9PT0pCwXIYQQiVXbZKShoYEmTZpAW1u78oNkMuTk5HAvXPl4jbk6StVy0lDRZ/PlJlqT\nUWlpqSgFIoQQ8nJQOVOZEELIq4ESAiGEEACUEAghhJShhEDIS6S1vj5kMpnKS2t9/fouKnkJ0VpG\nDQCN5CDqkvqzQp/Nl5voy1/XVUREBGxtbWFtbY01a9ZUuv/atWvo3bs3mjVrhrVr1/IuDiGEkGrU\nOFO5ruRyOQICAhAZGQkTExO4urpi1KhRsLOzE45p06YNNm7ciEOHDvEsCiGEEBW41hBiY2NhZWUF\nCwsLaGtrw9fXF2FhYUrHGBkZwcXFpcoJcIQQQqTDNSFkZGTAzMxMuG5qaoqMjAyeIQkhhLwgrk1G\nFZfProugoCDh/+7u7nB3dxft3IQQ0hhER0cjOjr6hR/PNSGYmJggPT1duJ6eng5TU9MXOlf5hEAI\nIaSyij+Wq9vorDpcm4xcXFxw48YNpKamoqioCHv37sWoUaOqPJaGrBFCSP3iPg/ht99+w7x58yCX\nyzF16lQsXrwYW7ZsAQDMmDED9+7dg6urK3JycqChoQE9PT0kJiZCV1f3f4WkeQjPjwMlzlcdzUMg\ntVHb706amNYA0B8dURclBFIbDW5iGiGEkJcDJQRCCCEAKCEQQggpQwmBEEIIAEoIhBBCylBCIIQQ\nAoASAiGEkDKUEAghhACghEAIIaQMJQRCCCEAKCEQQggpQwmBEEIIAEoIhBBCylBCIIQQAoASAiGE\nkDKUEAghhACghEAIIaQMJQRCCCEAKCEQQggpQwmBEEIIAEoIhBBCylBCIIQQAoBzQoiIiICtrS2s\nra2xZs2aKo+ZM2cOrK2t4ejoiLi4OJ7FIYQQUgNuCUEulyMgIAARERFITExEaGgorl69qnTM0aNH\ncfPmTdy4cQM//PADZs6cyas4tRIdHV3fReBK6ucnZbzG/NxeBY39/WvonxduCSE2NhZWVlawsLCA\ntrY2fH19ERYWpnTM4cOHMXnyZABAr1698OTJE9y/f59XkdTW0N+0umrMfwSN+bm9Chr7+9fQPy/c\nEkJGRgbMzMyE66ampsjIyFB5zO3bt3kViRBCSA24JQSZTKbWcYyxF3ocIYQQkTFOzpw5w4YOHSpc\nX7VqFfviiy+UjpkxYwYLDQ0VrtvY2LB79+5VOlenTp0YALrQhS50oUstLp06darV97YWOHFxccGN\nGzeQmpoKY2Nj7N27F6GhoUrHjBo1Cps2bYKvry/+/vtvtGrVCu3atat0rps3b/IqJiGEkDLcEoKW\nlhY2bdqEoUOHQi6XY+rUqbCzs8OWLVsAADNmzMCbb76Jo0ePwsrKCjo6OggODuZVHEIIISrIGKvQ\niE8IIeSVRDOVCSGEAODYZPSiSkpKMHjwYERFRUkWMzAwEDKZTBjxVPH/GzZskKwsYrK3t6/2PplM\nhoSEBFHjrV27tsZ48+fPFzVefUlOTsZrr72m8jaxXL58ucb3UmwLFy6stLJAVbeJRS6XQ1NTk8u5\nK9q/fz/Gjh2r8jYe5HI5nj59Cn19fW4xYmJi4OTkBF1dXYSEhCAuLg5z585Fx44d1Xp8g6shaGlp\nQUNDA0+ePJEsZmFhIS5evIjOnTvD2toacXFxKCoqgouLC3r06CF6PHt7ezg4OMDe3r7SxcHBQbQ4\nv/76a7WXw4cPixZHITc3F3l5eZUuubm5yM3NFT2egpeXF44cOYLS0lJuMcrz9vaudBvPL5SZM2fC\n1dUVmzdvRnZ2Nrc4CseOHat029GjR7nFs7a2xocffojExERuMRRWrVql1m1iGT9+PHJycvD06VPY\n29vDzs4OX375Jbd4M2fOhI6ODuLj4/HNN9+gU6dOmDRpktqPb3A1BADQ0dGBvb09Bg8eDB0dHQB8\nf6knJCQgJiYG2traAJ6/qH379hU6wMU2bNgwyGQy+Pn5gTGGXbt2AQBmzZpVaV5GXVhYWIh2LnUE\nBQVJGk9h5syZCA4ORmBgIMaNGwd/f3/Y2NiIHufq1atITExEdnY2fv75ZzDGIJPJkJOTg8LCQtHj\nKcTExODff//F1q1b4ezsjJ49e8Lf3x9DhgwRNc53332HzZs3IykpSalGkpubiz59+ogaq7xLly5h\nz549mDZtGuRyOd555x2MHz9e1F/Sv/32G44ePYqMjAzMmTNH+DvLzc0V/u55SExMhL6+Pnbt2oXh\nw4fjiy++gLOzMz766CMu8bS0tCCTyXDo0CHMnj0b06ZNw08//aT24xtkp/K2bdsA/G+SmuIPT7HM\nhdhsbGxw+vRptGnTBgDw+PFj9O7dG9evX+cSz8nJCZcuXVK6rXv37twW9ztz5gzmzJmDxMREFBUV\nQS6XQ1dXFzk5OVziFRQU4KeffkJiYiIKCgqE93Hr1q1c4ik8efIEe/bswcqVK2Fubo7p06dj4sSJ\nov3BHzp0CIcOHcKvv/6KUaNGCbfr6enB19cXbm5uosSpTklJCQ4dOoQ5c+agZcuWKC0txapVq6qs\nsbyI7OxsZGVlYdGiRVizZo3wpamnpyf8bfAWHR2NCRMmICsrC2PHjsVnn30GKyurOp83Pj4ecXFx\nWLJkCVasWCE8N319fQwcOBAGBgZ1jlGVrl274tKlS3j77bcxe/ZsuLu7w8HBQfTmWoX+/ftj2LBh\nCA4OxsmTJ2FkZAQnJydcvnxZvRPUataChJ4+fcquXr0qSaytW7cyc3NzNmnSJDZp0iTWsWNHFhwc\nzC2eg4MDO3nypHA9JiaGOTo6covn7OzM/v33X+bk5MRKSkrY1q1b2cKFC7nF8/b2Zp9++imztLRk\n27ZtY2+88QYLDAzkFo8xxjIzM9m6detYjx49mIeHBwsNDWWzZ89mAwYMED3W6dOnRT9nTS5dusTm\nzZvHrKys2MyZM9mFCxcYY4xlZGQwMzMz0eJkZ2czxp6/lo8ePap04aW4uJgdOnSIjR49mjk6OrK1\na9eyu3fvsv379zNra2tRYxUVFYl6PlW+/fZbZmxszIYNG8bkcjlLSUlhffv25Rbvzp077Ouvv2Z/\n/fUXY4yxW7dusW3btqn9+AaZEMLCwljnzp1Zx44dGWOMXbx4kXl4eHCNeefOHXbo0CF26NAhdvfu\nXa6xzp8/z+zt7Zm5uTkzNzdnDg4Owh85D87Ozowxxuzt7YXbeCYgxbkV8YqKiljPnj25xfP09GS2\ntrbs888/Z3fu3FG6T/HcxaCYaR8QEFDpwjPh9evXj23fvp09ffq00n3bt28XLc6bb77JGGOsY8eO\nzMLCotKFF0tLS+bv789OnTpV6b6AgABRYrz11luMMca6detW6VL+74K30tJSVlxcLFm82mqQfQhB\nQUE4e/YsBg4cCOB5c0pycjK3eKWlpYiMjERKSgqWLFmCtLQ0xMbGomfPnlzi9ejRAwkJCcjOzgZj\nDK1ateISR0FHRwfPnj2Do6MjPvroI7Rv317UvoqKmjRpAgBo2bIlLl++jPbt2+Phw4fc4s2ZM0f4\nrFR04cIF0eJ06dIFwPP3r3xzJsB3Da6//vqr2vtq02GoypEjRwAAqampop1THQkJCdDV1a3yvo0b\nN4oS49tvvwXwfKCFFMqPuKvqs8JrxN3BgwexaNEi3L9/Xymeus3DDTIhaGtrV/qS1NDgNyBq1qxZ\n0NDQQFRUFJYsWQJdXV3MmjUL58+f5xLv3r17+OSTT5CRkSHsF3HmzBlMnTqVS7yQkBCUlpZi06ZN\nWLduHW7fvo2DBw9yiQUA06dPx+PHj7Fy5UqMGjUKeXl5WLFiBbd4aWlp2LFjB4D/9TcB4n5ZAoCH\nhwcAYMqUKcJtcrkceXl5aNmypaixyrO0tKx0m0wm4/Yj6dSpU3B0dHzhoYu1FRgYWOk2mUwmap+T\nsbExAMDIyAjNmjWDpqYmrl+/juvXr2P48OGixVHIzc2tl4U6P/roI4SHh8POzu7FTlCf1ZPq+Pv7\ns507d7Ju3bqxf//9lwUEBLAZM2Zwi+fk5KT0L2PP2/l5GTp0KNuzZ49Sk0rXrl25xTtw4AArLCzk\ndv6KpK4Sz549W2i6mTZtGrO0tGTe3t7c4o0fP55lZ2ezvLw8Zmdnx4yNjdmaNWu4xXv48KFwSU9P\nZ+vWrWOffvopt3jdunVjcrmcXbp0iTk5ObGNGzey/v37c4u3f/9+duDAAXbgwAEWEhLCvLy8RGsq\nqqh79+7s6dOn7Pbt26xjx47srbfeYm+//TaXWMXFxWzt2rVczl0dNze3Oj2+QSaEvLw8tnjxYtaj\nRw/Wo0cP9vHHH7OCggJu8Xr27MlKSkqEhPDgwQOl5CC2Hj16MMaUExDPNv3JkyczMzMzNnHiRPbr\nr79y/8I2MzNj06dPZ5GRkay0tJRrrKpkZWWxIUOGcDu/4sfCzp072fz581lRURHr1q0bt3hV6d69\nO7dzKz6XQUFB7P/+7/+4x6tILpez119/ncu5Fc9tw4YNQhLn+ePPxcWF27mrMmfOHDZu3Di2e/du\nIckePHhQ7cc3yCaj5ORkrFq1iuuEkfICAwMxZswYPHjwAB9//DEOHDiAlStXcounq6uLR48eCdf/\n/vtvrk0O27ZtQ1FREX777TeEhoZi1qxZGDx4cK3GJ9fG1atXER4ejk2bNuGdd96Bh4cHfHx80K9f\nPy7xKmrRogVSUlK4nb+kpATFxcXCWG9tbW2uzQMXLlwQzl9aWorz589DLpdzi6enp4dVq1Zh586d\nOHnyJORyOYqLi7nFq+jff//l2ud05swZ7Nq1S/j885zQ2LdvXwQEBMDHx0eYUwUAzs7OXOJlZ2ej\nefPmlSYXenl5qfX4BpkQZs6ciWfPnsHf3x8TJkzg+mVZWloKS0tLrFmzBsePHwcAhIWFvXgbnBrW\nrl0LDw8PJCcnw83NDQ8fPsSBAwe4xQOed/QOHz4cGhoayM/Px6FDh7glBB0dHfj4+MDHxwdZWVmY\nM2cO3N3duX2JKdr2gefvZ2JiIsaNG8clFvB8pV4LCws4ODigf//+SE1N5foZXbBggZAQtLS0YGFh\ngX379nGLt3fvXuzevRtbt25F+/btkZaWhg8++IBbPF1dXeH5yWQytGvXjtsyGevXr8fq1asxZswY\ndO3aFUlJSdUOSBBDXFwcZDIZlixZonQ7r6V5FHO4XlSDnJgGQJiZuX//fm4zMxWqmijGi1wux4YN\nGxAYGIhr166BMQYbGxthZA4PR48exb59+xAVFQV3d3f4+PhgyJAh0NLi83uAMYY///wTe/fuRURE\nBFxdXeHj4yPaBKqKFPvUymQyaGlpwdzcXGlrVt4YY5DL5dxeT0JUWbNmDRYuXFhtB726qzw02IQA\n8J+ZqfDBBx/g9ddfh7e3tyQjA1xdXXHu3DnucRTGjx8PHx8fDBs2DM2aNeMez8LCAk5OTvDx8YGH\nh0e1QwrFdPfuXcTGxkJDQwOurq5o37696DFCQkLg5+eHtWvXSjqUMDMzE8uWLUNMTAxkMhn69euH\nJUuWiD57uE+fPjh16pTSL3aF2gxdrC3GGH7++WfExMRAQ0MDffv2xZgxY0SNMXfuXHz77bdKtUkF\nmUzGZW0vAFi2bJmwWGb517RijaGufv31V3h4eGDbtm1KcVgtV3lokD9p4uPjsW3bNoSHh2Pw4MEI\nDw+Hs7Mz7ty5I3xxi+n777/HN998A01NTeELk+cfQMV2RcWbxqNdsaSkBHfv3oWnp6fo566KYi0a\nsT/wNfnxxx+xfPlyoeofEBCAJUuWiD6MNz8/H4D0Qwp9fX0xYMAAYf2k3bt3w8fHB5GRkaLGOXXq\nFAAgLy9P1POqMmvWLCQlJWH8+PFgjOH777/HH3/8gc2bN4sWQzEEecGCBZXu4/le6ujoCOcvKChA\neHi4MJ9FTIpE179//0qr7sbGxqp/IlG7uEUi1czMmJgYxhjjOoKpKgMGDGDu7u6VLrwMGjSIZWVl\ncTt/RVKPrLC2tmaZmZnC9czMTNGXPCjv/v373M5dlaqGJPMc1RQQEFDlrGFebGxsmFwuF67L5XJm\nY2PDJZbUQ7ArKiws5DqEt3v37iw9PV24Hh0dXash7Q0yIUhFsayBVEPq1q9fzxhjSusYScHDw4OZ\nmpoyf39/SZZamDdvHps9ezb766+/2IULF4QLL71791b6Iy8sLGS9e/fmFs/a2poNHjyY/fjjj+zx\n48fc4ii8//77bPfu3UwulzO5XM727NnD5s+fzy1ecHAwGzZsGLO0tGQLFixg586d4xaLMcZGjBjB\nUlJShOspKSlsxIgRXGJJPQS7okePHtV64/vaiI2NZT169GB3795lR44cYQ4ODiwtLU3txzfIPgSp\nZmb26tULDg4OCAsLg6+vr9JyDjyW23Z0dER8fDzXlU2rIvXqse7u7lVWw8UeWaFYHiA+Ph4JCQlC\ns1hYWBgcHBywfft2UeOVd/bsWezZswdhYWHo0qULfHx84OfnJ2qM8m35T58+FWbrl5aWQkdHh+se\nEwDw6NEj/PzzzwgNDUVaWhpu3rwp6vkVzRw5OTnCUjEymQyxsbFwdXXFn3/+KWo8BcUQ7H379uHk\nyZNch2CXX0a8tLQUDx48wJIlS6rs/BXL6dOnMWPGDDRv3hzh4eFo27at2o9tkH0I5TtcCwsLceDA\nAaVx+2IJDw/H8ePHcezYMfTo0UP4omQVOoDE0qVLF1hbWyMjI6PSDlg8djBTmDJlCvLz85GWlgZb\nW1suMcpTjPrhTdGW36lTJ7z22mvCezZ69Gjubfy9evVCr1698Mknn+D999/H5MmTRU8I6rblX7ly\nBV27dhU1NgDcvHkT165dw61bt7i0eyva88vvUKjA8/2Tcgh2+bWTtLS00K5dO6Xl2B8/fozWrVvX\nOU7FzvKCggK0atUKU6dOrV2nOY9qCw88m3Xi4uJqvH/VqlWixbp79y6zt7dnqampLCUlRenCi9Sr\nx969e5e98847bOjQoYwxxq5cucJ+/PFHbvFUEXsZhCdPngjNKlZWVuzDDz9k58+fFzVGbYg9q/7D\nDz9kVlZWbMiQIWzr1q2S9j9VRcxZy0eOHGGTJ08Wlrs/cuRIva4+KtZ7FxUVVekSHR0t/KuuBpkQ\nzp8/L7Q7nzt3jn333Xdcp5erwnMZi6p4eXmJer7u3buzrKwspefBc+0kqddqUkXs98/CwoLNnTuX\nnT59ul6W5qhI7Of3/fffs4cPH1Z7/z///CNqPFXEfH6+vr7sl19+kXwgSXXEfu+SkpJYfn6+cD0/\nP58lJyer/fgG2WQk9czMhkbsvhKpV4/NzMyEj48PvvjiCyF+Y5q0lZSUVOPrFxgYKNqyzfVhxowZ\nNd4/ceJESfvAxBQaGlrj/b1798aZM2ckKo34xo4dq1R+DQ0NjBs3Tu15Tw3yr1SqNuhXRdeuXbFr\n1y6UlJTgxo0b2LBhA9ftHqVeq0lqqpJpTEyMRCUhYuO5N7YU5HK50qoHTZs2RVFRkdqP5/czsQ4y\nMzMRGBiI7t27w9nZGXPnzuXSqfyq2LhxI65cuYKmTZsKm5evX7+eW7yKazX5+fmJPmKL/E/Tpk3r\nuwikgTA0NERYWJhwPSwsDIaGhuqfQNQGLJH85z//YcuXL2fJycksKSmJrVixgv3nP//hFq/8pKaq\nfP7559xiV0XsdsV9+/apdZtYCgoKWFFREbt8+TJLSEhgz549k6TNtqqJjIwxrvtjV0Xs92/QoEFq\n3SYVHn1qKSkp7I8//mCMPX8fFfs7M8ZYQkKC6PGqI/Zzq2pvap57Vd+4cYP17NmTmZqaMlNTU/b6\n66+zGzduqP34BpkQpJ6ZaWVlxd566y125MgRSToJFRPUqrstIiJC1HhVfch5dpRXNSKM5yixU6dO\nMTs7O2ZqasoYez5qbObMmdziqSLWa5ufn88yMzOZvb290hdISkoKt5m86ujVq5eo59uyZQtzcXFh\nr732GmOMsevXr9dbwhP776Jjx45MJpOx1q1bs9atWzOZTCbsWW1paSlqrPJyc3NZTk5OrR/XIBOC\n1DMz5XI5+/3335mPjw977bXX2KJFi9j169e5xavqQ8djg5yjR4+ygIAAZmRkxAIDA4VZypMnT2au\nrq6ix7tz5w47f/48s7GxYRcuXBBGi0VFRXH9AnN1dWW3bt1Sel27dOnCLZ4C7xrJunXrmIWFBWvS\npInSZvf29vZs48aNosSoitQ1EgcHB1ZYWKj0/vH8AShlbWTatGnsyJEjwvWjR4+y6dOnixqjvLoO\n+W5QCUFHR4fp6uoyXV1dJpPJmKamJtPU1GQymYzp6upKUobjx4+zDh06MH19fda/f39R13TZvXs3\nGzlyJGvZsiUbOXKkcBkwYACXP7hLly6x4OBgZmZmxrZt28aCg4NZcHAwO3jwIJclF7Zt28bc3d2Z\nrq6u0hpNHh4etdq1qbYUyU2qLVClrpFs2LCB27nLq68aScX3r7i4WBiyLDapayNVtXY05CHfDSoh\n1JeHDx+y9evXM2dnZzZ8+HB28OBBVlRUxM6dOydM5hJDamoqi4qKYr169RImjURFRbHz589znRxT\nVFTE7dxV2b9/v6TxvL29WUxMDHNycmLPnj1jX331FfPx8eEWT+oayd69e4Xq//Lly9mYMWO4rA1V\nXzWSDz74gK1cuZJ17tyZHTt2jHl6erKPP/6YSyypayODBw9mK1asYCkpKSw5OZmtXLmS6/audd2e\nt0EmhJiYGJabm8sYY2zHjh3s/fffZ6mpqdziWVtbs2XLllW5CNTq1au5xZXKyZMn2RtvvMGsrKyE\nP3Ke7ZcFBQVs586dbOXKlWzZsmUsKCiILVu2jFu8Bw8esPHjxzMjIyNmaGjI3n77bZUDBepC6hqJ\n4gvr5MmTbMCAAezXX3/l0uSnIFWNRKGkpIRt2bKFeXt7M29vb/bDDz9w68uTsjbC2PMBK4GBgczJ\nyYk5OTmxOXPmiN6RXN6AAQNYZmam8PzOnDlTq9VVG+Q8hPfeew/x8fGIj4/HN998g6lTp2LSpEnc\nFru6fv16tWunLFq0SLQ49bUBydSpU7F+/Xo4OztDU1OTS4zyRo8ejVatWqFHjx6SbMhjZGSE3bt3\nc4+jYG5uLuwdUFRUhA0bNnDdclXxnoWHh2P69OkYOXIkPvvsM27x2rVrh9zcXOjp6WHFihWIi4vD\np59+ym0fYE1NTbz77rt49913uZy/vAEDBuDzzz9Hfn6+sOdCVZvmiKVNmzaSDrmu6/a8DXK1U8Vq\noMuWLYOJiQmmTZsGZ2dnXLx4kUu8qvZUlclkOHHiBJd4UuvVqxfOnj0rWbxu3brhn3/+kSxecnIy\nNm7ciNTUVJSUlADguwvWw4cPMXfuXERGRoIxhiFDhmDDhg2i72CmMGLECJiYmOCPP/5AXFwcmjVr\nhl69eiE+Pp5LPHt7e1y+fBkxMTH49NNP8cEHH2D58uW122hFzTjV4bXYo1wux08//SRsQj906FBM\nmzZN9MX06muHNgAoLi7G9evXAQA2NjZKi+mp0iATQv/+/TFs2DAEBwfj5MmTMDIygpOTEy5fvswl\n3vnz54X/FxYW4uDBg9DS0sJXX33FJV5SUhJMTEzQrFkzREVF4fLly5g0aVKl5SXEsmjRIsjlcnh5\neSlNYuL1i+/dd99FQEAAHBwcuJy/IgcHB0ybNg3dunUTZhHLZDIMGDBAkvi8PX36FBEREXBwcIC1\ntTXu3r2Ly5cvc99jfNGiRbC3t8eECRO4LNmemppa4/0WFhaixpPShQsX0KNHj2pXXXB3d+cW+9Sp\nU8KPI0WiU+wYp0qDTAh3797F7t270bNnT/Tr1w9paWmIioritn5/VXjue+zo6IgLFy4gNTUVb775\nJkaPHo0rV67g6NGjXOJJtT+Bgp2dHW7evAlLS0shAfFc3rtnz56i/3qtidQ1EoUHDx4oLa1gbm7O\nJY7UNRIAuHfvHs6ePcttT+z6qI3Uh4kTJyI5ORlOTk5KzcPqrq3VIBOC1B4/fiz8v7S0FOfPn8fc\nuXOFapfYFL+2vvzySzRv3lxYpuNlXTCsoup++fH6xRcSEoKkpCQMHTpUkhqQ1DWSw4cPY8GCBbhz\n5w7atm2LW7duwc7ODleuXOEST+oaScU9saOjo0XfE7u+aiMxMTFYtmxZpR8PYi9gqWBnZ4fExMQX\nbgJrUJ3K9dXp6uzsXGl1VV4bZgDPN+jYvXs3duzYIWygUVxcLHqckJAQ+Pn5Ye3atUqvJyvbAGj+\n/PmixsvJyYG+vj709fVFPa8qV65cQUhICKKiopQWnuNVA2rWrBnmzJnD5dxV+fTTT3HmzBkMHjwY\ncXFxiIqKQkhICLd4Ojo68Pb2xoMHD5CWlgYAXDdW+vLLLxEXFyf0wTx69Ai9e/cWNSGU/8LnXRsp\nT+oBHd26dcPdu3dhbGz8Qo9vUAlBMXJD3Z2ixJKYmIjNmzcjJiYGGhoa6Nu3L1xcXLjF27p1K77/\n/nt88sknsLS0RHJyMiZOnCh6nPz8fAD/21mMt/Hjx+PIkSNKCVaB56+i/fv3IyUlRWmVR54CAwMR\nFBQkWY1EW1sbhoaGKC0thVwux8CBAzF37lwusQDpaySGhobQ1dUVruvq6tZuQbZaqFgbCQgIEL02\nUl6rVq0wfPhwLucuT9F5nZeXhy5duqBnz55KzbXqNmdSkxGeryGur6+PiRMngjGG3bt3Izs7G/v3\n7w99EB0AAA9BSURBVK/vokli9erVWLx4sWTxxN7y0dPTE1u2bEG7du1EO2dNFi1ahJCQEFhZWUlS\nI3njjTfwyy+/YPHixcjMzETbtm1x/vx5nD59mks8BwcHnDhxolKNZOvWrVzi+fn54Z9//sHo0aMB\n/G9PbAcHB9Frsp07d8aZM2cq1Ub+/fdf0WKUV35Ah+IHi0wmE/3Hg6LzurrtSNVtzqSEgOd7HScm\nJqq8ra7Gjh2L/fv3V9nBVZ8dW1L3X4gdb8CAAUhISICrq+sL/SqqrU6dOuHq1auS1Ujy8vLQvHlz\nlJaWYteuXcjJycGECRO4DXPt0aMHLly4AEdHR1y8eBGamppwcHDg9vkMCgoC8L99lFmFPc2XLl0q\nWiw3NzdERUUJn5Nnz55h4MCB3JKr1EPak5OT0aFDBzRv3hzA872V7927B0tLS7Ue36CajOqLs7Mz\nzpw5g969ewN4vqFLjx49RI+jmKAyZcoU9OrVC2ZmZgBQKaOT2lm2bJmk8ezt7ZGVlSVZjUTRnKKp\nqYkpU6Zwj2dgYIDc3Fz069cPEyZMQNu2bZWadMSmSAhS6NSpE15//fVKtRFFP5vY/Wo8h5dWpVHu\nmCYVxS/1kpIS9OnTB2ZmZpDJZEhLS4ONjY3o8Tp06ADgeZv+jBkzYGBgAF9fX4wdO1ayL5fGSOo/\nuqysLNja2nKvkVQ1uEKB5yCLQ4cOoXnz5li3bp1QIxHzV7pCfUze6tSpEzp16iS8rqNHj4ZMJuPW\nb6mjoyPEKiwsRHh4ONdZ7XXdMe2VbjKqaSiaTCZDx44ducaPj4/Hvn37cODAAZiamuL48eNc41Xn\nZW0yqq9RafUx2agxqmnyVmOaWFjes2fPMGTIEG7L8LzxxhsIDAxUqgFt2LBB7e+WV7qGUN8zIdu2\nbYv27dujTZs2ePjwIbc4jx49qrG9eezYsdxiV0WsLR/ra1RaY/3il7pGomiWvXTpEubNm6d03/r1\n60VNCPW5lER5T58+RUZGBrfzf//995gwYQICAgIAAKamprUaovxK1xDqy+bNm7Fv3z48ePAAY8eO\nhY+PD7p06cItnrW1NZycnODv74/hw4dzH4Lq4eGB8ePHY/To0dDR0eEaC3g+SqXih76q2+qqvmok\njV1VNUbF8hliqa/aSPkBJKWlpXjw4AGWLFmCwMBALvEUcnNzAQB6enpKt2/fvr3GFR8oIdSDxYsX\nw8fHB05OTpLEKy0tRWRkJLZu3Ypz585h3Lhx8Pf3R+fOnbnEi46Oxt69e3H06FG4uLhg/PjxGDly\nJLeVTyt+oZSUlMDBwUH0UWJEXKGhodi9ezdOnjyJfv36Cbfn5uZCU1OTSxPq+vXrq6yNVLxNLOWb\npbW0tNCuXbtaLTYnNpXNtXVdf5u8XHjuCFdRcXExO3bsGBs7dizT09MT/fyff/4509XVZZqamsJO\ne7q6uszAwIAtXLhQ9HgKEydOVOs2UrP62DBKqu1rGypVe0ZTDeEVkJmZiV27dmHHjh1o164dpk2b\nBg8PD8THx+Ott95Suc7LiygoKMDhw4exb98+XLhwAR4eHmovsFVbixYtwhdffFHt/WJPhKMaycun\nPmojDZGqGsIr3an8qnBzc8PEiRNx6NAhYe4DALi4uOC9994TPd64ceNw9uxZDBs2DAEBARgwYIDS\njF6x1ZQMgOcrQIoxqmnVqlVYvXo1CgoKlNpmtbW1JdncpbGRshPbzc0NHTp0wMOHD/HBBx8Ic3/0\n9PTg6OgoWpyXHdUQXgGswsxP3nbs2AFPT0/o6+tLsuOWKmIPq5W6RkKIWAICArBp06Zq76eE8AqQ\nevq8VDtuqetlnWfxqlCsqFqRmPs91NckP6llZWVhx44dlZbbVncbT2oyegWU3/mt/I5wvEi9BzB5\nub355ptKs3lTUlJgY2Mj6uqqUs9VqS9vvvkmevfuDQcHB2hoaNS6dYASwiug4lLeffv2haurK7d4\nJiYmePfdd/HHH39g0aJFKCwsRGlpKbd4qog1EY7wUXH/7YsXL+K///0vl1hS1Ebq07Nnz/DNN9+8\n8OOpyegVIPWOcFLtuHXhwgVhud+qfgU1lj6LV1G3bt0qJQqxzsu7NlKfvv76a+jr68PDw0Pph1Dr\n1q3VejzVEF4BUu8Ip9hxS6FDhw7Cwn5iWrBgAWQyGQoKCnDhwgU4ODgAABISEuDi4qK06qOUqEZS\nO2vXrhX+X1paiosXL8LExIRLLClrI/WhWbNm+PDDD/H5558rbe+q7uZUlBBeAVLvCCcVxTIEXl5e\n+L//+z9hmYB//vmHy+qc6tZI/v77b9FjN2bld/TT0tLCyJEjlX5Q8OTs7IyzZ89KEksKa9euRVJS\n0gvvOEdNRq+Axr4jnFQbHLm7uzfIGsnL7ty5c1i1alWlkTE8NuSpqjby+PFj/P7776LHqg9DhgzB\nL7/88sJriFEN4RVw5coVpS/HQYMGcV1MT2oODg6YNm2aUsLjMdlI6hrJq2LChAn4+uuv0a1bN64T\nGIH6rY1IoUWLFnBycsLAgQOV9uqgYadEINWOcPUlODgY3333Hb799lsAQP/+/TFz5kxu8a5du6a0\nimW3bt1w9epVbvEaO0NDQ4waNUqSWCNGjKhUG1mzZk29bV8rNk9PT3h6eirdVpthp9Rk1IiV3xHu\n+vXrlXaEa0xfYvn5+UhLS4OtrS33WL6+vtDV1VWqkeTl5SE0NJR77Mbo2LFj2Lt3L9544w2ljei9\nvLxEj9W5c+cqayP1vTdKQ0EJoRGr7x3hpHL48GF8+OGHePbsGVJTUxEXF4elS5dy2/SkoKAA3333\nHU6ePAngfzUSXst7N3YTJkzA9evX0bVrV6Uv6eDgYNFjubm54fTp06Kft6GwtLSsdFttRhlRQiAv\nPWdnZ5w4cQIDBw4Uxv/zGseuIGWNpLGzsbHBtWvXJFlvS8raSH3IzMwU/l9YWIgDBw7g0aNHWLFi\nhVqP59uDQ4gEtLW10apVK6XbeHZOHj58GN27d8ewYcMAAHFxcZK1gTdGbm5uki0dvn37dsTHxyMi\nIgLh4eEIDw/Hr7/+KklsKRgaGgoXU1NTzJs3D0eOHFH78dSpTF56Xbt2xa5du1BSUoIbN25gw4YN\ncHNz4xYvKCgIZ8+eFRYN7N69u9pVclLZmTNn4OTkBEtLS6WRMTw6es//f3v3F9JUG8cB/Dso/2RG\nRAjuUkQ2MZFODjXSSNm6qMCLrRQj6q6Bt64UIiJLb6yUROuiEBFcISwiIwqMClzboC5SRw1kBUF1\nZW4zxjpd1M5b+b60V/c8vo/v93O3A4evF8KP73nOeZ5gUFobWQvpb2UAIJVKIRQKIZVKZXw/BwIp\nb2BgAN3d3cjNzUVLSwscDofQzfRkN5L17v79+9Ky0m1kvW5Pnv56H/hrVwKv15vx/VxDIOXdunUL\nTqfzj9ey5cSJE2hsbERPTw8mJibQ39+PZDKJoaEhIXmUPRaLBZFIREobWQvp3Yx//8jvzJkzGd3P\ngUDK+7vN5ERuMBeLxdDd3Y0HDx4AgNFI+JbRf98/vXm3Xl47dTgc2Lp1KzRNM7ahB743h0xwIJCy\nJicnce/ePYyPj+PIkSPGsYifP3/GzMyMsAN5ZDcSokyt9u06PvgkZZnNZmiahry8PGiaBk3TsGvX\nLhw6dEjo3jQXLlzI6BqRbHV1dat6/MWGQMpbWFhAQUGBUZFTqRS+fPmCTZs2ZTVnrRoJUaasVive\nvHmz4jUSvmVEyrPb7Xj48CE2b94M4PtHYw6HI+tfpKYbic/ng6ZpxjbYhYWFuHTpUlaziFZicnJy\nVfezIZDyqqqq8OLFiz9eyxZZjYRINq4hkPIKCgoQCoWM38FgEPn5+cLy7HY7EomE8Tsej6OpqUlY\nHpEsfGREyrt8+TKcTifMZjMA4P379xgfHxeWt7S0ZDyeAoDCwkLE43FheUSycCCQ8qqrqxEOhxEO\nh6HrOiwWCzZu3CgsL91I0mdKiG4kRLJwDYGUF4vF0NfXh2g0iuvXr+P169cIh8M4cOCAkLxAIIDD\nhw8vayTr4Zxq+n/jQCDluVwuaJqGkZERvHr1CrFYDHV1dXj58qWwzGQyKa2REMnCRWVSXiQSgcfj\nMfa3X+kB45mKxWLo6enBlStXsGPHDszPz+Pu3btCM4lk4EAg5eXm5v7y1k8kEjE+yhHh+PHjyMnJ\nMb5zMJvN6OrqEpZHJAsHAinv7Nmz2L9/P969e4fW1lbs27cPvb29wvJkNxIiWfiWESnPbrdj586d\n8Pv90HUd/f392L59u7A82Y2ESBYOBFKerut4/Pgxnj59CpPJhGQyiebmZmF5vzeSZ8+e4ebNm8Ly\niGThW0akvJMnTyISiaClpQW6rsPr9aKkpASDg4PCMj99+mQ0kpqaGqGNhEgWDgRSnsViwczMjHGM\n5devX1FeXo65uTkhebquY2Jiwmgke/bsEdpIiGThojIpr7S0FNFo1PgdjUZRWloqLM/tdmN4eBiV\nlZWoqKjA8PAw3G63sDwiWdgQSHn19fUIBAKw2WwwmUx4/vw5qqursWXLFphMJty5cyerebIbCZEs\nXFQm5Z07d27ZNZPJZJxXkG3pRpI+h1d0IyGShQOBlFdUVITy8vJfrk1NTWHv3r1C8hYWFmC1Wpc1\nkoMHDwppJESy8JERKa+iogJHjx5FR0cHEokEPB4PAoEApqenheRNTU0tu/ZzI2loaBCSSyQaGwIp\nz+/3w+PxoLa2FouLi2htbc368Zk/k91IiGThW0akvA0bNiA/Px+JRAJLS0soKSkxFnxFcLlc6O3t\nha7riMfjaG9vx6lTp4TlEcnCgUDKs9lsyMvLQzAYxJMnTzA2Ngan0yksz+/34+3bt6itrYXNZkNx\ncbHQRkIkCwcCKe/atWsoKyvDxYsXUVxcjIGBAVRWVgrLk91IiGThfzEp78aNG5iensbY2BiA72cc\n+3w+YXmyGwmRLBwIpDy/34+rV68a5xpv27YNyWRSWJ7sRkIkCwcCKS8nJwepVMr4/fHjR6GPcGQ3\nEiJZOBBIee3t7WhubsaHDx/Q2dmJ3bt34/Tp08LyZDcSIln4HQIpr62tDZqm4dGjRwAAn88Hq9Uq\nLE92IyGShV8qE/1Lo6Oj8Hq9CIVCOHbsGG7fvo3z58/D5XKt9Z9GtCocCEQrMDs7azSSxsZGoY2E\nSBYOBCIiAsBFZSIi+oEDgYiIAHAgEBHRDxwIREQEgAOBiIh++Ab7VTQ5n7EhmgAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b829d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "The tree gives us a useful tool for analying feature importance\n",
    "'''\n",
    "fig, ax = plt.subplots()\n",
    "width=0.35\n",
    "#ax.bar(train.drop(lab,1).columns.values, clf.feature_importances_, width, color='r')\n",
    "ax.bar(np.arange(13), clf.feature_importances_, width, color='r')\n",
    "ax.set_xticks(np.arange(len(clf.feature_importances_)))\n",
    "ax.set_xticklabels(train.drop(lab,1).columns.values,rotation=90)\n",
    "plt.title('Feature Importance from DT')\n",
    "ax.set_ylabel('Normalized Gini Importance')\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 0
}
